Problem: Solve for $x$ : $2x^2 - 2x - 180 = 0$
Explanation: Dividing both sides by $2$ gives: $ x^2 {-1}x {-90} = 0 $ The coefficient on the $x$ term is $-1$ and the constant term is $-90$ , so we need to find two numbers that add up to $-1$ and multiply to $-90$ The two numbers $9$ and $-10$ satisfy both conditions: $ {9} + {-10} = {-1} $ $ {9} \times {-10} = {-90} $ $(x + {9}) (x {-10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x -10) = 0$ $x + 9 = 0$ or $x - 10 = 0$ Thus, $x = -9$ and $x = 10$ are the solutions.